标题： 基于数据的方法估计密度水平集的比较仿真研究 显示英文标题

标题： A comparative simulation study of data-driven methods for estimating density level sets

摘要： 密度水平集的估计主要使用以下三种方法之一：插入法、超额质量法或混合方法。 插入法基于用某种非参数估计量（通常是核估计量）替换未知密度。因此，从实用角度来看，带宽选择是一个基本问题。 最近，已经提出了特定于水平集的选择器。 然而，如果有一些关于水平集几何形状的先验信息可用，则超额质量算法可能很有用。 在这种情况下，不需要密度估计量，并且可以避免带宽选择的问题。 第三种方法是其他两种方法的混合。 与超额质量方法一样，它假设水平集具有温和的几何限制，并且像插入方法一样，需要一个密度的先导非参数估计量。 一个有趣的开放问题是这些方法的实际表现如何。 在这项工作中，回顾了现有方法，并提出了两种新的混合算法。 通过广泛的模拟比较了它们的实际表现。 显示英文摘要

摘要： Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus, the bandwidth selection is a fundamental problem from a practical point of view. Recently, specific selectors for level sets have been proposed. However, if some a priori information about the geometry of the level set is available, then excess mass algorithms can be useful. In this case, a density estimator is not necessary, and the problem of bandwidth selection can be avoided. The third methodology is a hybrid of the others. As in the excess mass method, it assumes a mild geometric restriction on the level set and, like the plug-in approach, requires a pilot nonparametric estimator of the density. One interesting open question concerns the practical performance of these methods. In this work, existing methods are reviewed, and two new hybrid algorithms are proposed. Their practical behaviour is compared through extensive simulations.